A note on some discrete valuation rings of arithmetical functions

Emil D. Schwab and Gheorghe Silberberg

Address. E.D.Schwab, Department of Mathematics, University of Oradea, str. Armatei Romane nr. 5, 3700 Oradea, ROMANIA


Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas, 79968-0514, USA

Gheorghe Silberberg, Department of Mathematics, University of Timisoara, bd. V. Parvan nr. 4, 1900 Timisoara, ROMANIA

E-mail: c98sig01@student.ceu.hu

Abstract. The paper studies the structure of the ring A of arithmetical functions, where the multiplication is defined as the Dirichlet convolution. It is proven that A itself is not a discrete valuation ring, but a certain extension of it is constructed,this extension being a discrete valuation ring. Finally, the metric structure of the ring A is examined.

AMSclassification. 13F30

Keywords. Discrete valuation ring, arithmetical function, Dirichlet convolution